Question

A computer database uses a binary sequence of 5 bits to represent unique user IDs. To increase the number of unique IDs that the database is able to represent, the database administrator increases the number of bits in a user ID to 12 bits. How many times more unique user IDs can be represented with the new system?

Answer 1

Increasing the number of bits in a user ID from 5 to 12 allows the database to represent 128 times more unique user IDs.

Step-by-step explanation:

When the database administrator increases the number of bits in a user ID from 5 bits to 12 bits, the number of unique user IDs that can be represented is multiplied by 2 raised to the power of the difference in the number of bits. In this case, the difference is 12 - 5 = 7.

So, the number of times more unique user IDs that can be represented with the new system is calculated as 2^7 = 128. Therefore, the new system can represent 128 times more unique user IDs than the original system.